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1 %DEMMLP1 Demonstrate simple regression using a multi-layer perceptron
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2 %
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3 % Description
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4 % The problem consists of one input variable X and one target variable
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5 % T with data generated by sampling X at equal intervals and then
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6 % generating target data by computing SIN(2*PI*X) and adding Gaussian
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7 % noise. A 2-layer network with linear outputs is trained by minimizing
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8 % a sum-of-squares error function using the scaled conjugate gradient
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9 % optimizer.
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10 %
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11 % See also
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12 % MLP, MLPERR, MLPGRAD, SCG
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13 %
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14
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15 % Copyright (c) Ian T Nabney (1996-2001)
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16
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17
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18 % Generate the matrix of inputs x and targets t.
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19
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20 ndata = 20; % Number of data points.
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21 noise = 0.2; % Standard deviation of noise distribution.
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22 x = [0:1/(ndata - 1):1]';
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23 randn('state', 1);
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24 t = sin(2*pi*x) + noise*randn(ndata, 1);
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25
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26 clc
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27 disp('This demonstration illustrates the use of a Multi-Layer Perceptron')
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28 disp('network for regression problems. The data is generated from a noisy')
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29 disp('sine function.')
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30 disp(' ')
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31 disp('Press any key to continue.')
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32 pause
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33
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34 % Set up network parameters.
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35 nin = 1; % Number of inputs.
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36 nhidden = 3; % Number of hidden units.
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37 nout = 1; % Number of outputs.
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38 alpha = 0.01; % Coefficient of weight-decay prior.
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39
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40 % Create and initialize network weight vector.
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41
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42 net = mlp(nin, nhidden, nout, 'linear', alpha);
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43
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44 % Set up vector of options for the optimiser.
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45
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46 options = zeros(1,18);
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47 options(1) = 1; % This provides display of error values.
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48 options(14) = 100; % Number of training cycles.
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49
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50 clc
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51 disp(['The network has ', num2str(nhidden), ' hidden units and a weight decay'])
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52 disp(['coefficient of ', num2str(alpha), '.'])
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53 disp(' ')
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54 disp('After initializing the network, we train it use the scaled conjugate')
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55 disp('gradients algorithm for 100 cycles.')
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56 disp(' ')
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57 disp('Press any key to continue')
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58 pause
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59
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60 % Train using scaled conjugate gradients.
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61 [net, options] = netopt(net, options, x, t, 'scg');
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62
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63 disp(' ')
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64 disp('Now we plot the data, underlying function, and network outputs')
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65 disp('on a single graph to compare the results.')
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66 disp(' ')
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67 disp('Press any key to continue.')
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68 pause
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69
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70 % Plot the data, the original function, and the trained network function.
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71 plotvals = [0:0.01:1]';
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72 y = mlpfwd(net, plotvals);
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73 fh1 = figure;
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74 plot(x, t, 'ob')
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75 hold on
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76 xlabel('Input')
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77 ylabel('Target')
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78 axis([0 1 -1.5 1.5])
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79 [fx, fy] = fplot('sin(2*pi*x)', [0 1]);
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80 plot(fx, fy, '-r', 'LineWidth', 2)
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81 plot(plotvals, y, '-k', 'LineWidth', 2)
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82 legend('data', 'function', 'network');
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83
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84 disp(' ')
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85 disp('Press any key to end.')
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86 pause
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87 close(fh1);
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88 clear all;
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